O filtro gaussiano possui apenas um parâmetro livre, que é a frequência de corte da filtragem (que basicamente dá a largura do filtro).

Reading the data¶

Lately, the .fits data was transformed into .csv and saved in database/csv_files. We are going to import a light curve sample and work with it.

[2]:

FILE_PATH = '/content/drive/MyDrive/01 - Iniciação Científica/02 - Datasets/csv_files/EN2_STAR_CHR_0101086161_20070516T060226_20071005T074409.csv'

[3]:

import pandas as pd

data_sample = pd.read_csv(FILE_PATH)
display(data_sample)

	DATE	WHITEFLUX
0	2007-05-16 18:10:55.071642	112626.77
1	2007-05-16 18:19:27.113766	112605.61
2	2007-05-16 18:27:59.155929	112771.50
3	2007-05-16 18:36:31.198092	113113.60
4	2007-05-16 18:45:03.240256	112621.79
...	...	...
23946	2007-10-05 19:08:02.358665	112438.61
23947	2007-10-05 19:16:34.313684	112406.01
23948	2007-10-05 19:25:06.268742	112496.13
23949	2007-10-05 19:33:38.223801	112344.83
23950	2007-10-05 19:42:10.178859	112318.50

23951 rows × 2 columns

[4]:

import numpy as np

x = data_sample.DATE.to_numpy()
y = data_sample.WHITEFLUX.to_numpy()

Gaussian Transfer Function¶

The transfer function of a Gaussian 1-D lowpass filter (GLPFs)

$H(u) = e^{-D^2(u)/2D^2_0}$

where $D(u)$ and $D_0$ was defined on 03 - Ideal Lowpass Filters.ipynb.

Note. The cutoff frequency must be given in Nyquist.

[5]:

cutoff_freq = 0.2

[6]:

def gaussian_array(array, fourier_transform, cutoff_freq):
  # Extrating information of the signal
  n_time = len(array)
  D0 = cutoff_freq * n_time
  xc = n_time

  # Creating the filter array
  len_filter = len(fourier_transform)
  filter = np.zeros(len_filter)

  for i in range(len_filter):
    filter[i] = exp( (-(i-(xc-1.0))**2)/(2*((cutoff_freq * n_time)**2)) )

  return filter

Choosing the best Gaussian parameters¶

On filters module, we can pass gaussian on the filter_technique and it will makes all the procedures for the Butterworth Lowpass filter.

[7]:

from tools import *

Plotting different cutoff frequencies¶

[8]:

cutoff_freqs = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]

[22]:

i = 0
cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[23]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[24]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[25]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[26]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[27]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[28]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[29]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1

[30]:

cutoff_freq = cutoff_freqs[i]

Filter = new_filters.FrequencyDomainFiltering()
Filter.filter(array=y, filter_technique='gaussian', numExpansion=70, cutoff_freq=cutoff_freq, order=None)
y_filtered = Filter.getFiltered
title = f"Gaussian filter with Cutoff frequency = {cutoff_freq}"
new_viz.view_filter_results(x, y, x, y_filtered, title=title)
print()
i += 1